In this paper, instead of using the peaks of the spherically-averaged structure factor following the Debye scattering equation as in Ref. niu2018molecular, we propose to use the full three-dimensional structure factor (SF).
This has two important advantages.
On one hand, it provides a more accurate description by resolving each scattering vector into its three-dimensional components. This avoids the degeneracy intrinsic to the Debye peaks, which can lead to mislabeling defected structures. On the other hand, the SF is also computationally more efficient, since it scales linearly with the number of atoms. However, an inevitable hurdle of this choice is that the 3D SF presents a number of crystal peaks much greater than its spherically-averaged counterpart. Thus it becomes crucial to avoid the lengthy procedure of Ref. niu2019temperature and replace it by a modern machine learning (ML) technique, in which several descriptors are non-linearly combined to produce efficient CVs.[1]}, [2]}
To this effect, we use the Deep Linear Discrimination Analysis (Deep-LDA) method[2]} and obtain a Deep-LDA CV that we then use in the On-the-fly Probability Enhanced Sampling (OPES) method[4]}, [5]} to simulate the crystallization of multicomponent and molecular systems. As prototypical examples, we have applied with success our approach to study the crystallization of NaCl and CO\(_2\)  from their liquid phase. We have chosen these systems since they present a number of challenges as discussed in the literature.[6]}, [7]}, [8]}, [9]}
